KINETIC FRICTION: F = ma and W= methods

1. Pull the block with the wide wood surface down along the table by the tension, T, in a string connected over a pulley to a mass M. At the same time measure the position of the block with the motion detector (Notice that the useful range of detection is only about 0.5 m, so carefully choose the collection rate for best quality data).

The tension T is obtained from Newton's second law applied to the hanging mass (Weight down - Tension up = ma). Notice that for this expression to be true the string pulling the block along the table must be horizontal (you might have to adjust the pulley's height to satisfy this condition):

m_H g -T = m_H a ==> T = m_H (g - a)

where a is the joint acceleration of the block and hanging mass.

Newton's second law applied to the block will give:

If we eliminate the tension T:

(Eq. Method I)

METHOD II. WORK - ENERGY METHOD

1. The work done by the applied force (the tension T) over a distance d is

Notice that for this expression to be true the string pulling the block on the table must be horizontal (you might have to adjust the pulley's height to satisfy this zero angle condition).

Choose two points along the path. The distance between them is d. The tension T is calculated as in Method I. Find the work done on the cart by the applied force between those two points.

2. Now using the definition of kinetic energy , determine the difference in the cart's kinetic energy () between those two points.

3. In general: Sum of all works = Change of Kinetic Energy (Work-Energy theorem, Chapter 7):

where is the magnitude of the work done by the friction force along a distance d:

.

So the Work-Energy Theorem indicates thatcan be used to determine the coefficient of friction between the block and the table.

μ_k = (W_T -ΔK)/ (m_B g d) (Eq. Method II)

where:

W_T = T d

ΔK = 1/2 m_B v_f² - 1/2 m_B v_i²

with T = m_H (g - a),

where d is the distance between the initial and final positions chosen, and v_i and v_f are the speeds at those positions.

2) You will use both methods discussed to calculate the experimental value of the coefficient of friction μ_k between the block and the table for each of the 4 orientations of the block.

For each orientation obtain μ_k for 2 values of the hanging mass.

Also for the two "flat orientations" add a 100 g mass on top of the block and obtain μ_k for each of the two values of the hanging mass.

Calculate your results for both methods in Excel.

Submit a detailed sample calculation for each method with your report.

In your Discussion be sure to indicate whether or not the coefficient of friction depends on the following parameters and, if so, how:

(1) the contact area; (2) the mass of the block; (3)  the hanging mass; (4)  the material in contact with the table; (5)  the particular region of the table being used and (6)  the speed of the block? 

Did you find any significant differences between Methods I and II for the coefficient of friction results? If so, which method is better and why?